More likely is that Clifton just sang both. They appear to be distinct songs, unrelated even by parody. We have at least a partial first line for JBG's "The Convivial Man"--"They tell me"--which contrasts with Clifton's "Hey for fun and jokery" in both tone and rhythm. From the latter line, one might guess that the song was about a convivial man, but the word "convivial" never appears in the lyrics of "The Commercial Man".

As a side note, the Bodley broadside for "The Commercial Man" says it was sung to "Strike for Tyrol and Liberty" (the most famous theme from Rossini's William Tell, also known as the Lone Ranger theme).